In data collection, we refer the input/output trajectory
\((y_t, u_t), t=0,\cdots ,T-1\)  as a rollout. There are two approaches to collect the data. The first method involves multiple rollouts [1]}, [2]}, [3]}, [4]}, where the system is run and restarted with a new input signal \(N\)  times. The second approach is the single rollout method [5]}, [6]}, [7]}, [8]}, [9]}, where an input signal is applied from time 0 to \(N \times T -1\)  without restart. As this paper only focuses on the realization step of the problem, we can use either of aforementioned methods for data collection.
